Question

A coin is flipped and a six-diced die is rolled. What is the probability that the coin lands heads and the die shows four or more? (Hint: define A to be the event ‘coin lands heads’ and B to be the event ‘die shows four or more’. A and B are independent events, since the coin flip has nothing to do with the coin toss. The probability that both events will occur is the product of the two individual probabilities.)

(a) 0.5

(b) 1

(c) 0.25

(d) 0.75

(e) none of the above

Answer 1

(c) 0.25

Explanation:

Probabilities of Independent Events

If the occurrence of an event A has no influence on the ocurrence of an event B, then both events are called as independent. The probability of ocurrence of two independent events is the product of both probabilities.

The probability that a coin lands heads is 1/2.

The probability that a die shows four or more is 3/6 or 1/2 since there are 3 favourable outcomes out of 6 possible outcomes.

The probability that both events occur is 0.5*0.5=0.25

Answer: (c) 0.25