Let's work through this problem step by step.
1. Given Data:
- The probability that the dice lands on a 6 is [tex]\( P(\text{lands on 6}) = 0.38 \)[/tex].
2. Calculating the Probability that the Dice Does Not Land on 6:
- The probability that the dice does not land on 6 can be calculated as:
[tex]\[
P(\text{does not land on 6}) = 1 - P(\text{lands on 6})
\][/tex]
- Substituting the given value:
[tex]\[
P(\text{does not land on 6}) = 1 - 0.38 = 0.62
\][/tex]
So, the probability that the dice does not land on 6 is [tex]\( 0.62 \)[/tex].
3. Number of Rolls:
- The dice is rolled 150 times.
4. Expected Number of Times the Dice Does Not Land on 6:
- To find the expected number of times the dice does not land on 6, multiply the probability of not landing on 6 by the total number of rolls:
[tex]\[
\text{Expected number of times not landing on 6} = P(\text{does not land on 6}) \times \text{number of rolls}
\][/tex]
- Substituting the values:
[tex]\[
\text{Expected number of times not landing on 6} = 0.62 \times 150 = 93.0
\][/tex]
Therefore, the expected number of times the dice does not land on 6 when rolled 150 times is 93.
