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Question

Lewis rolls a number cube that has sides labelled 1 to 6 and then flips a coin. The probability that Lewis rolls an even number and flips a head is .

A
14
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B
12
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C
34
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Solution

The correct option is A 14
Sample Space Diagram:
1 2 3 4 5 6
Hesads (H) H1 H2 H3 H4 H5 H6
Tails (T) T1 T2 T3 T4 T5 T6

Total number of possible outcomes= 12=2×6=row×column

Let A is an event of rolling an even number (E) and flipping a head (H).

Favorable Outcomes for event A= {H2, H4, H6}

Number of favorable outcomes to the event A = 3

P(A)=Number of outcomes favorable to ATotal number of possible outcomes

P(A)=312=14


Alternative method–––––––––––––––––––

Suppose, P(E), P(H) and P(E and H) are the probabilities of rolling an even number on die, flipping a head on coin and rolling an even number and flipping a head, respectively.

We know,
P(E and H) = P(E)×P(H)

Now, to find P(E and H), we need to find out P(E) and P(H).

Total number of possible outcomes for rolling a die= 6

Favorable outcomes to the event E= {2, 4, 6}
Number of outcomes favorable to event E= 3

P(E)=Number of outcomes favorable to event ETotal number of possible outcomes
P(E)=36=12

Flipping a coin has two possibilities= {H, T}
Probability of flipping head= P(H)=12

Finally,
Probability that Lewis rolls an even number and flips a head = 12×12=14


The probability of rolling an even number and flipping a head is 14.







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