To determine the probability of selecting a transmission in good condition, given that it is an automatic transmission, we need to follow these steps:
1. Identify the total number of automatic transmissions:
- The table summarizes the number of automatic transmissions for each condition. To find the total number of automatic transmissions, we sum these values:
[tex]\[
\text{Total automatic transmissions} = 248 + 152 + 108 + 56 + 36 = 600
\][/tex]
2. Identify the number of automatic transmissions in good condition:
- From the table, the number of automatic transmissions in good condition is given as 108.
3. Calculate the probability:
- The probability of an event is given by the ratio of the favorable outcomes to the total possible outcomes.
- Here, the favorable outcomes are the automatic transmissions in good condition, and the total possible outcomes are the total number of automatic transmissions.
[tex]\[
\text{Probability} = \frac{\text{Number of automatic transmissions in good condition}}{\text{Total number of automatic transmissions}}
\][/tex]
- Substituting the values we identified:
[tex]\[
\text{Probability} = \frac{108}{600}
\][/tex]
4. Simplify the fraction:
- To simplify the fraction, we divide the numerator and the denominator by their greatest common divisor (GCD). The GCD of 108 and 600 is 12:
[tex]\[
\frac{108 \div 12}{600 \div 12} = \frac{9}{50} = 0.18
\][/tex]
Thus, the probability of selecting a transmission in good condition, given that it is an automatic transmission, is [tex]\( 0.18 \)[/tex] or 18%.
By following these steps, we see that:
- The total number of automatic transmissions is 600.
- The number of automatic transmissions in good condition is 108.
- The probability of selecting a transmission in good condition, given that it is an automatic transmission, is 0.18 or 18%.
