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Popular Word Problems >

A fair coin is flipped four times. Use a tree diagram to find the probability of observing exactly two heads.Enter your answer as a percentage, to the nearest percent.

Solution

A f ai r co in i s f l i pp e d f o u r t im es . U se a t ree d ia g r am t o f in d t h e p ro babi l i t y o f o b ser v in g e x a c tl y tw o h e a d s . E n t er yo u r an s w er a s a p erce n t a g e, t o t h e n e a res t p erce n t .

Solution

\frac{3}{8}

+1

Decimal

0.375

Solution steps

The possible outcomes when a coin is thrown four times are

2 \cdot 2 \cdot 2 \cdot 2

Therefore, the number of possible outcomes:

2^{4}

Find the number of favorable outcomes of observing exactly 2 heads.:

6

Probability

= \frac{number of favorable outcomes}{total number of outcomes}

= \frac{6}{2 ^{4}}

\frac{6}{2 ^{4}} = \frac{3}{8}

= \frac{3}{8}

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