Probability

1 )

A bag contains 8 apples and 6 orange. Four fruits are drawn out one by one and not replaced. What is the probability that they are alternatively of different fruits?

10/143

15/120

20/143

26/110

None of these

View Solution

Answer :

Fruits can be drawn in two formats AOAO and OAOA

Apple drawn 1st P=8/14*6/13*7/12*5/11

Orange drawn 1st P=6/14*8/13*5/12*7/11

Adding both we get

2[8*7*6*5/14*13*12*11]=2*(10/143)=20/143.

2 )

In an interview the probability of Praveen to got selected is 0.4. The probability of Geetha to got selected is 0.5. The probability of Sam to got selected is 0.6. The probability of Suresh to got selected is 0.8. What is the probability that at least 2 of them got selected on that day?

0.806

0.632

0.688

0.732

None of these

View Solution

Answer :

Required probability=1 - no one got selected - 1 got selected

No one got selected = (1- 0.4) x (1- 0.5) x (1- 0.6) x (1- 0.8) = 0.024

1 got selected= 0.4 x ((1-0.5) x (1-0.6) x (1- 0.8) ) + 0.5 x ((1-0.4) x (1-0.6) x (1-0.8)) +0.6 x ((1-0.4) x (1-0.5) x (1-0.8)) + 0.8 x ((1-0.4) x (1-0.5) x (1-0.6))

= 0.016 + 0.024 + 0.036 + 0.096 = 0.17

So, Required probability = 1 - 0.024 - 0.17 = 0.806

3 )

A basket contains 10 red ball and 15 white ball. out of which 3 red and 4 white balls are damaged. If two balls selected at random, what is the probability that either both are white balls or both are not damaged?

203/435

313/300

317/400

203/300

None of these

View Solution

Answer :

P(A) = 15c2 / 25c2, P(B) = 18c2 / 25c2

P(A∩B) = 11c2 / 25c2

P(AUB) = P(A) + P(B) - P(A∩B) => (15c2 / 25c2)+( 18c2 / 25c2) - ( 11c2 /

25c2) = 406/600 =>203/300

4 )

A box contains tickets numbered from 1 to 16. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 4?

19/240

11/240

43/250

9/80

None of these

View Solution

Answer :

From 1 to 16, there are 4 numbers which are multiple of 4

1st 2 are multiple of 4, and one any other number from (16-4) = 12 tickets 4c2*12c1/16c3 = 72/560 2nd all are multiples of 4. 4c3/16c3=4/560

Add both 72/560+4/560=76/560

5 )

Chance that Sheela tells truth is 35% and for Ramesh is 75%. In what percent they likely to contradict each other in the same question?

9/40

15/25

25/40

23/40

None of these

View Solution

Answer :

P(A) = 35/100=7/20 and P(B) = 75/100=3/4.

Now they are contradicting means one lies and other speaks truth.

So,

Probability = 7/20*1/4 + 13/20 * 3/4 =7/80+39/80=46/80=23/40

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