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A girl flips a coin and rolls a 6-sided die 50 times. The outcome that she gets a tail and rolls a 1 occurs 7 times. Calculate the experimental probability and the theoretical probability of having the outcome of tail and 1 .

A girl flips a coin and rolls a $6$ -sided die $50$ times. The outcome that she gets a tail and rolls a $1$ occurs $7$ times. Calculate the experimental probability and the theoretical probability of having the outcome of tail and $1$ .

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Find probabilities using the addition rule

Full solution

Q. A girl flips a coin and rolls a

6

-sided die

50

times. The outcome that she gets a tail and rolls a

1

occurs

7

times. Calculate the experimental probability and the theoretical probability of having the outcome of tail and

1

.

Calculate Experimental Probability: Experimental probability is calculated by dividing the number of times an event occurs by the total number of trials. Specifically, it is given by the formula $\frac{\text{number of times an event occurs}}{\text{total number of trials}}$ .
Perform Coin and Die Trials: The girl flips the coin and rolls the die $50$ times, and the event of getting a tail and rolling a $1$ occurs $7$ times.
Calculate Experimental Probability: Calculate the experimental probability: $P(\text{Tail and 1}) = \frac{\text{Number of times Tail and 1 occurs}}{\text{Total number of trials}} = \frac{7}{50}$ .
Determine Theoretical Probabilities: The theoretical probability of getting a tail is $\frac{1}{2}$ , since a coin has two sides.
Determine Theoretical Probabilities: The theoretical probability of rolling a $1$ on a $6$ -sided die is $\frac{1}{6}$ , since there are $6$ possible outcomes.
Calculate Theoretical Probability: The theoretical probability of both events happening together (getting a tail and rolling a $1$ ) is found by multiplying the probabilities of each independent event: $P(\text{Tail}) \times P(1) = \frac{1}{2} \times \frac{1}{6}$ .
Calculate Theoretical Probability: The theoretical probability of both events happening together (getting a tail and rolling a $1$ ) is found by multiplying the probabilities of each independent event: $P(\text{Tail}) \times P(1) = \frac{1}{2} \times \frac{1}{6}$ .Calculate the theoretical probability: $P(\text{Tail and 1}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$ .

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