A die is cast twice and a coin is tossed thrice. Find the probability that the die will turn a 5 each time and the coin will turn a head every time.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1/288.
Case I:
The probability of a die rolling a 5-on-one roll,
P(5 on the dice) = 1/6
Since the dice is cast twice, the probability of rolling a 5 both times,
P(5 Twice) = (1/6)2 = 1/36
Case II:
Probability of getting a head-on one toss,
P(Head on coin) = 1/2
The coin is tossed three times, the probability of getting a head each time,
P(Head thrice) = (1/2)3 = 1/8
We know that, the events are independent
Probability of getting 5 twice and heads thrice = P(5 Twice) × P(Heads thrice)
⇒ 1/36 × 1/8 = 1/288