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1 answer:
Answer:
P = 0.5207
Step-by-step explanation:
First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.
Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).
So, the probability that just the first card is a diamond or an ace is calculated as:
At the same way, the probability that just the second card is a diamond or an ace is:
Finally, the probability that both cards are diamonds or aces is:
Therefore, the probability that at least one of the cards is a diamond or an ace is:
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It would take Sarah 0.15 years more than Brandon to get $1,530 in her account.
Step-by-step explanation:
Step 1; First, we need to calculate the interest per year for both Brandon and Sarah.
For Brandon, if 3 % is compounded monthly, then yearly interest = 3.75 × 12 = 45% is compounded yearly. So 0.45 × $510 = $229.50 is compounded annually.
For Sarah, if 3 % is compounded monthly, then yearly interest = 3.625 × 12 = 43.5% yearly. So 0.435 × $510 = $221.85 is compounded annually.
Step 2; If money is three times $510, there would have to be a balance of 3 × $510 = $1,530. As they have already invested $510.
The money needed by interest = $1,530 - $510 = $1,020.
Step 3;
As Brandon gets $229.50 every year, years taken to get $1,020 = = 4.4444 years.
As Sarah gets $221.85 every year, years taken to get $1,020 = = 4.5977 years.
The difference in years = 4.5977 - 4.4444 = 0.1533 years. Rounding this off to the nearest hundredth, we get 0.15 years.