1. A bank received 3 bad cheques per day what is the probability that in a particular day the bank will receive (I)no bad cheque (II)at least 2 bad cheques (iii) at most 1 bad cheque.

2. In a manufacturing company,for every 15 bulbs produced 3 were found defective.if 5 bulbs were produced,find the probability that (I)none is defective (II)at most 4 are defective (iii) at least 4 are defective

3. Two coins were tossed once,what is the probability that
(I) exactly two tails appear?
(II) at least two tails appear?
(III) at most three tails appear?

4. The marks scored by 1000 candidates in a test are normally distributed with a mean mark of 50 and a variance of 16,find the number of candidates whose marks are
(I) below 25
(II) above 45
(III) between 25 and 45

5.In a sta 203 exam 60% of the student passed,if a random num of 3 students were selected for investigation.what is the probability that
1.no student passed
2. Atleast one student passed
3. At most one student passed
4. No student failed
5. Atleast one student failed
6. Atmost no student failed

This questions are base on probability in statistics

please I need help on this question

adebayo18015:
1. A bank received 3 bad cheques per day what is the probability that in a particular day the bank will receive (I)no bad cheque (II)at least 2 bad cheques (iii) at most 1 bad cheque.

2. In a manufacturing company,for every 15 bulbs produced 3 were found defective.if 5 bulbs were produced,find the probability that (I)none is defective (II)at most 4 are defective (iii) at least 4 are defective

3. Two coins were tossed once,what is the probability that
(I) exactly two tails appear?
(II) at least two tails appear?
(III) at most three tails appear?

4. The marks scored by 1000 candidates in a test are normally distributed with a mean mark of 50 and a variance of 16,find the number of candidates whose marks are
(I) below 25
(II) above 45
(III) between 25 and 45

5.In a sta 203 exam 60% of the student passed,if a random num of 3 students were selected for investigation.what is the probability that
1.no student passed
2. Atleast one student passed
3. At most one student passed
4. No student failed
5. Atleast one student failed
6. Atmost no student failed

omoh I no sure say I go get time to solve all,
(2)
15 produced,3 defective
probability of defective bulbs=0.2
probability of good bulb=1-(0.2)=0.8
p=0.2
q=0.8
the probability of there being a defective bulb is 0,1,2...5 is given by successive terms of (q +p)^5
In a sample of 5,
the probability of no defective bulb=
q^5=(0.^5=0.32768
(ii)
at most 4= probability of 0,1,2,3,4
probability of zero defective=q^5=0.32768
probability of one defective =5q⁴p
=5(0.8⁴)(0.2)
=0.4096
two defective=10q³p²
=10(0 .8³)(0 2²)
=0.2048
three=10q²p³
=10(0.8²)(0.2³)
=0.0512
four=5qp⁴
=5(0.(0.2⁴)
=0 0064
at most 4
=0+1+2+3+4(defective bulbs)
=0.32768+0.4096+0.2048+0.0512+0.0064
=0.99968
(iii)at least 4
=sum of probability of having 1,2,3,4,5 defective bulbs
=5q^5p + 10q³p² + 10q²p³+5qp⁴+p^5
already solved all except p^5 which is equal to (0.2)^5
=0.00032
therefore, probability of at least 4 defective bulbs equals the sum of having 1...5 defective bulbs
=0.4096 + 0.2048 + 0.0512 + 0.0064
+ 0.00032
=0.67242

adebayo18015:
1. A bank received 3 bad cheques per day what is the probability that in a particular day the bank will receive (I)no bad cheque (II)at least 2 bad cheques (iii) at most 1 bad cheque.

2. In a manufacturing company,for every 15 bulbs produced 3 were found defective.if 5 bulbs were produced,find the probability that (I)none is defective (II)at most 4 are defective (iii) at least 4 are defective

3. Two coins were tossed once,what is the probability that
(I) exactly two tails appear?
(II) at least two tails appear?
(III) at most three tails appear?

4. The marks scored by 1000 candidates in a test are normally distributed with a mean mark of 50 and a variance of 16,find the number of candidates whose marks are
(I) below 25
(II) above 45
(III) between 25 and 45

5.In a sta 203 exam 60% of the student passed,if a random num of 3 students were selected for investigation.what is the probability that
1.no student passed
2. Atleast one student passed
3. At most one student passed
4. No student failed
5. Atleast one student failed
6. Atmost no student failed

(3)
When we toss two coins simultaneously then the
possible of outcomes are: (two heads) or (one
head and one tail) or (two tails) i.e., in short (H,
H) or (H, T) or (T, T) respectively; where H is
denoted for head and T is denoted for tail.
(i)
the outcomes are (H,H),(H,T),(T,T),(T,H)(total number of outcome is 4)
probability of getting exactly two tails =1/4
(ii)
atleast 2 tails
at most 2 tails
I think there's a mistake in the question it should be 3 coins

adebayo18015:
1. A bank received 3 bad cheques per day what is the probability that in a particular day the bank will receive (I)no bad cheque (II)at least 2 bad cheques (iii) at most 1 bad cheque.

2. In a manufacturing company,for every 15 bulbs produced 3 were found defective.if 5 bulbs were produced,find the probability that (I)none is defective (II)at most 4 are defective (iii) at least 4 are defective

3. Two coins were tossed once,what is the probability that
(I) exactly two tails appear?
(II) at least two tails appear?
(III) at most three tails appear?

4. The marks scored by 1000 candidates in a test are normally distributed with a mean mark of 50 and a variance of 16,find the number of candidates whose marks are
(I) below 25
(II) above 45
(III) between 25 and 45

5.In a sta 203 exam 60% of the student passed,if a random num of 3 students were selected for investigation.what is the probability that
1.no student passed
2. Atleast one student passed
3. At most one student passed
4. No student failed
5. Atleast one student failed
6. Atmost no student failed

(5)
60% passed
p(passed)=0.6
p(failed)=0.4
q=passed
p=failed
probability is given by successive terms of (q+p)³
=q³ +3q²p +3qp² +p³
none failed(all passed)=q³=0.6³=0.216
one failed(two passed)=3q²p=3(0.6²)(0.4)=0.432
two failed (one passed)=3qp²=3(0.6)(0.4²)=0.288
three failed (none passed)=p³=0.4³=0.064
in probability,
at least = greater than or equal to
at most= less than or equal to
(i)none passed (all failed)
=p³=0.4³=0.064
(ii) at least one passed equals probability of 1,2,3 passed= 0.288 + 0.432 + 0.216=0.936
(iii)at most one passed
=p(0 passed) + p(one passed)
=0.064+0.288=0.352
(iv) at least one failed
=p(1 failed) + p(2 failed) + p( 3 failed)
=0.432 + 0.288 + 0.064
=0.784
(v)at most none failed
=q³=0.216
will drop the remaining solution if I'm chanced tonight

Spartancosta:

(5)
60% passed
p(passed)=0.6
p(failed)=0.4
q=passed
p=failed
probability is given by successive terms of (q+p)³
=q³ +3q²p +3qp² +p³
none failed(all passed)=q³=0.6³=0.216
one failed(two passed)=3q²p=3(0.6²)(0.4)=0.432
two failed (one passed)=3qp²=3(0.6)(0.4²)=0.288
three failed (none passed)=p³=0.4³=0.064
in probability,
at least = greater than or equal to
at most= less than or equal to
(i)none passed (all failed)
=p³=0.4³=0.064
(ii) at least one passed equals probability of 1,2,3 passed= 0.288 + 0.432 + 0.216=0.936
(iii)at most one passed
=p(0 passed) + p(one passed)
=0.064+0.288=0.352
(iv) at least one failed
=p(1 failed) + p(2 failed) + p( 3 failed)
=0.432 + 0.288 + 0.064
=0.784
(v)at most none failed
=q³=0.216
will drop the remaining solution if I'm chanced tonight

Thank you sir for interest in helping solve this problem. I really appreciate. More knowledge and grace to you sir.

adebayo18015:


Thank you sir for interest in helping solve this problem. I really appreciate. More knowledge and grace to you sir.

Amen boss

adebayo18015:
1. A bank received 3 bad cheques per day what is the probability that in a particular day the bank will receive (I)no bad cheque (II)at least 2 bad cheques (iii) at most 1 bad cheque.

2. In a manufacturing company,for every 15 bulbs produced 3 were found defective.if 5 bulbs were produced,find the probability that (I)none is defective (II)at most 4 are defective (iii) at least 4 are defective

3. Two coins were tossed once,what is the probability that
(I) exactly two tails appear?
(II) at least two tails appear?
(III) at most three tails appear?

4. The marks scored by 1000 candidates in a test are normally distributed with a mean mark of 50 and a variance of 16,find the number of candidates whose marks are
(I) below 25
(II) above 45
(III) between 25 and 45

5.In a sta 203 exam 60% of the student passed,if a random num of 3 students were selected for investigation.what is the probability that
1.no student passed
2. Atleast one student passed
3. At most one student passed
4. No student failed
5. Atleast one student failed
6. Atmost no student failed

(1)
the question is a question on poisson distribution
p(X=x)= (¥^x * e^-¥)/x!
¥= lambda
(i) no bad cheques
p(3,0)=(3^0 * e^-3)/0!
p(no bad cheques=0.0498
(ii) at least 2 bad cheques
= probability 2 and 3 bad cheques
p(3,2)=3² * e^-³/2!
=0.2240
p(3,3)= 3³ * e^-³/3!
=0.2240
p(at least 2 bad cheques)=0.2240 + 0.2240
=0.448
(iii) at most one bad cheque
=p(0) +p(1)
p(3,0)=0.0498
p(3,1)= 3¹ * e^-³/1!
=0.1494
p(at most one bad cheque)= 0.0498 + 0.1494
=0.1992