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# What is the probability of obtain tails and an odd number? # What is the probability of obtain tails and an odd number?

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Probability and combinatorics asked 2020-10-20
What is the probability of obtain tails and an odd number?

## Answers (1) 2020-10-21
The coin has 2 possible outcomes: heads H and tails T/ The die has 6 possible outcomes: 1, 2, 3, 4, 5, 6.
There are then $$\displaystyle{2}\cdot{6}={12}$$ possible outcomes of flipping the coin and rolling the die: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6.
# of possible outcomes = 12
We note that 3 of the 12 possible outcomes result in tails and an odd number: T1, 73, T5.
# of favorable outcomes = 3
The probability is the number of favorable outcomes divided by the number of possible outcomes:
P(tails and odd) = # of favorable outcomes /# of possible outcomes Te hie outcomes > $$\displaystyle=\frac{{3}}{{12}}=\frac{{1}}{{4}}={0.25}={25}\%$$

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