Q7. Suppose a year has 366 days. Randomly pick 2 people from a party, what is th
ID: 3069688 • Letter: Q
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Q7. Suppose a year has 366 days. Randomly pick 2 people from a party, what is the probability that these two people are born on the same day? (Same means months and date are the same, ages don't need to be the same) (2 points in total) Probability Q8. Researchers at the Stony Brook University School of Medicine have determined that children under 2 years old who sleep with the lights on have a 31% chance of becoming myopic before they are 16. Children who sleep in darkness have a 74% probability of not becoming myopic. A survey indicates that 27% of children under 2 sleep with some light on. Find the probability that a random child under 2 will become myopic before reaching 16 years old. (2 points in total) Probability Q9. A password is consisting of 8 characters. And user must choose these 8 characters from either 10 digits (0-9) or 26 letters (a-z) or 3 special characters (1?-). If the password must end with a special character and avoid starting with numbers. How many valid password could be made here ?(Write out the formula and do not need to calculate the exact number) (2 points in total) Possible Ways Q10. 3 letters are equally randomly selected from 26 English letters (a-z) and arranged into a word, what is the probability that this word is "boy"? (2 points in total) ProbabilityExplanation / Answer
dear student, please post the question one at a time.
7)
No. of days in a year = 366
Since there are two birthdays(A and B) in a year,
n(S) = 366 x 366 -----------(1)
b) Let E be the event that A and B have different birthdays.
But of 366 days A can have a birthday on any day and hence B can have a birthday on (366 - 1) i.e. 365 days.
n(E) = 366 × 365
Now, P(E) = n(E) / n(S) = (366x365) / (366x366) = 365 / 366.
a) Let F be the event that both of them have their birth days on same day.
E and F are complementary events.
P(F) = 1 - P(E)
Using value of P(A) from (i),
P(F) = 1 – 365 / 366 = 1 /366
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