Harsh has $a$ number of girlfriends and Bixby has $b$ number of girlfriends. $30\%$ of $a$ are female and $50\%$ of $b$ are male. Whats the probability that I get two females if I pick one randomly each from $a$ and $b$ ?

Full solution

Q. Harsh has

a

number of girlfriends and Bixby has

b

number of girlfriends.

30\%

a

are female and

50\%

b

are male. Whats the probability that I get two females if I pick one randomly each from

a

and

b

Calculate Female Percentage: Determine the percentage of females in Harsh's group. Since $30\%$ of ' $a$ ' are female, we can calculate the percentage of females as $100\% - 30\% = 70\%$ .
Convert to Probabilities: Determine the percentage of females in Bixby's group. $\newline$ Since $50\%$ of ' $b$ ' are male, we can calculate the percentage of females as $100\% - 50\% = 50\%$ .
Calculate Combined Probability: Convert the percentages to probabilities. $\newline$ The probability of picking a female from Harsh's group is $\frac{70}{100}$ or $0.7$ . $\newline$ The probability of picking a female from Bixby's group is $\frac{50}{100}$ or $0.5$ .
Perform Multiplication: Calculate the probability of picking one female from each group. $\newline$ To find the combined probability of two independent events, we multiply the probabilities of each event. $\newline$ Probability of picking one female from Harsh's group AND one female from Bixby's group = $0.7 \times 0.5$ .
Perform Multiplication: Calculate the probability of picking one female from each group. $\newline$ To find the combined probability of two independent events, we multiply the probabilities of each event. $\newline$ Probability of picking one female from Harsh's group AND one female from Bixby's group = $0.7 \times 0.5$ .Perform the multiplication to find the final probability. $\newline$ $0.7 \times 0.5 = 0.35$ .