Aaron sold half of his comic books and then bought sixteen more. He now has 36. With how many did she begin?
1 answer:
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Answer:
The probability that Leon strikes is greater than Carlton strike is 0.40905
Step-by-step explanation:
From the question, we have;
The percentage of Carlton's rolls are strikes, = 70%
The number of games Carlton played, n₁ = 25
The percentage of Leon's rolls that are strikes, = 67%
The number of games Leon played, n₂ = 25
Therefore, we have;
Where;
k₁ = 0.7 × 25 = 17.5
k₂ = 0.67 × 25 = 16.75
The test statistic is given as follows;
From the z-table, we have;
The p-value for Carlton strikes is greater than Leon's strike = 0.59095
∴ The p-value for Leon strikes is greater than Carlton strike = 1 - 0.59095 = 0.40905
The probability that Leon strikes is greater than Carlton strike = 0.40905
Answer:
a) 0.64
b) 0.21
c) 0.79
Step-by-step explanation:
Percentage of industrial-grade diamonds = 80%
This means, if one diamond is chosen at random, there is 80% chance that it will be of industrial-grade. So,
P(Industrial grade) = 80% = 0.80
Part a)
Probability that 1st diamond is industrial-grade = 0.80
Since, selection of diamonds in independent, the probability that 2nd diamond is also industrial grade = 0.80
The overall probability of both diamonds being industrial-grade will be the product of their individual probabilities, according to the fundamental rule of counting.
So, if two diamonds are chosen at random, the probability that both are industrial grade = 0.80 x 0.80 = (0.80)² = 0.64
Part b)
Following the same logic as we followed in the previous part.
The probability of each of the 7 diamonds being industrial-grade is 0.80, so the probability that all 7 are industrial grade will be:
Probability = 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = = 0.21
So, if 7 diamonds are chosen at random, the probability that all 7 are industrial grade is 0.21.
Part c)
The event "at least one" is complement of event "none". So, the event "at least one of 7" will be complement of "none of the 7"
If none of the selected diamonds is gem quality, this means all 7 of the diamonds are industrial-grade. So,
The probability that none of the diamonds is gem-quality = The probability that all 7 are industrial-grade = 0.21
So,
The probability that at least one of the 7 selected diamonds is gem-quality = 1 - Probability that none is gem-quality
= 1 - 0.21
= 0.79
Since the probability that atleast one of the 7 randomly selected diamonds is gem-quality is greater than 0.05, it won't be unusual event.