Question

# Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square. OR A game consists of tossing a coin 3 times and noting its outcomes each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Open in App
Solution

## The sample space of the given experiment is: S=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)⎫⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎬⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎭ ∴ n (S)= 36 Let E be the event that the product of numbers obtained on the upper face is a perfect square ∴ E = {(1,1), (1,4), (2,2), (3,3), (4,1), (4,4), (5,5), (6,6)} ∴ n (E) = 8 P(E)=n(E)n(S)=836=29 OR The set of possible outcomes of the given experiment are: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Let E be the event of getting three heads or three tails. ∴ E = {HHH, TTT} ∴ Probability of winning = P (E) =n(E)n(S)=28=14 ∴ Probability of losing = P(E') = 1 - P (E) =1−14=34 Therefore, the probability that Hanif will lose the game is 34

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Experimental probablity
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program