Cognizant Probability Quiz-1

Required probability = P(A) x P(B)
= (7/8) x (9/10)
= 63/80

n(S) = Number of ways of drawing 2 balls out of 13 = 13C2 = 13 x 12 / 2= 78
n(E) = No. of ways of drawing 2 balls out of 5 = 5C2 = 5 x 4 / 2 = 10

∴ P(E) = n(E)/n(S) = 10/78 = 5/39

n(S) = (2)3 = 8
E = Event of getting 0, or 1 or 2 heads
= {TTT, TTH, THT, HTT, HHT, HTH, THH}
⇒ n(E) = 7
∴ P(E) = n(E)/n(S) = 7/8

Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
∴ Required probability = 1/5 x 2/3 + 4/5 x 1/3
= 2/15 + 4/15
= 6/15
= 2/5 Ans.

If the last digit is 1,3,7,9 in the product then we can only select numbers whose last digit is 1,3,7 or 9 from 0,1,2,.....9
Probability that a selected number ends
with 1,3,7 or 9 = 4/10=2/5
Probability of selecting four such numbers =(2/5)⁴
=16/625​

Total ways = 52
There are 13 cards of diamond, 4 cards of king, but one card is king of diamond which
is counted both in diamond and king cards
⇒ Favourable ways = 13 + 4 - 1 = 16
∴ Required probability = 16/52 = 4/13

Probability of getting head in one trail = 1/2
∴ Reqd Probability of getting heads in both the trails = 1/2 x 1/2 = 1/4

Solution:

Total fruits in the basket = (3 + 2 + 6) = 11

Event of selecting an apple = n (E) = 3

Therefore, P(E)= n(E)/n(S) = 3/11

Total number of cards n(S) = 52
Number of red cards n(E) = 26
∴ P(E) = n(E)/n(S) = 26/52 = 1/2

Assuming we're using standard fair 6-sided dice.

There are a total of 6×6=36 possible rolls.

There are two ways to roll an 11: (5,6),(6,5)

And so the odds of rolling an 11 are:

2/36=1/18Ans.