give each probability as a simplified fraction, decimal (up to 4 decimal places), and percent(up to 2…
give each probability as a simplified fraction, decimal (up to 4 decimal places), and percent(up to 2 decimal places). a month of the year is chosen at random. january, february, march, april, may, june, july, august, september, october, november, and december. find each probability. a) p(starts with j) b) p(starts with t) c) p(has at most 30 days)
Answer
Explanation:
Step1: Determine total number of months
There are 12 months in a year, so the total number of possible outcomes $n(S)=12$.
Step2: Calculate probability of starting with J
The months starting with J are January, June, July. So $n(A) = 3$. The probability $P(A)=\frac{n(A)}{n(S)}=\frac{3}{12}=\frac{1}{4}=0.25 = 25.00%$.
Step3: Calculate probability of starting with T
The months starting with T are 0. So $n(B)=0$. The probability $P(B)=\frac{n(B)}{n(S)}=\frac{0}{12}=0 = 0.00%$.
Step4: Calculate probability of having at most 30 days
The months with at most 30 days are April, June, September, November. So $n(C)=4$. The probability $P(C)=\frac{n(C)}{n(S)}=\frac{4}{12}=\frac{1}{3}\approx0.3333 = 33.33%$.
Answer:
a) $\frac{1}{4}$, $0.25$, $25.00%$ b) $\frac{0}{12}$, $0$, $0.00%$ c) $\frac{1}{3}$, $0.3333$, $33.33%$