Answer :
6/16 or 3/8 or 0.375 they’re all the same answer btw just simplified
Answer:
The probability = [tex]\displaystyle\bf\frac{3}{8}[/tex]
Step-by-step explanation:
To find the probability that two coins land heads up, we use the Probability Formula:
[tex]\boxed{P(A)=\frac{n(A)}{n(S)} }[/tex]
where:
- [tex]P(A)[/tex] = probability of event A
- [tex]n(A)[/tex] = number of outcomes of event A
- [tex]n(S)[/tex] = number of all outcomes
Since each coin has 2 outcomes: H (head) and T (tail), then the total outcomes of tossing 4 coins will be:
[tex]n(S)=2\times2\times2\times2\ (or\ 2^4)[/tex]
[tex]\bf n(S)=16[/tex]
Let A = 2 coins land heads up, then
A = {(HHTT), (HTHT), (HTTH), (THHT), (THTH), (TTHH)}
[tex]\bf n(A)=6[/tex]
*Tips*
For subject that only has 2 equal outcomes, we can find the total of outcomes using Pascal Triangle. As the event tosses 4 coins, we use the 4th row of Pascal Triangle, which is 1, 4, 6, 4, 1, which means:
- total outcomes of 0 Head = 1
- total outcomes of 1 Head = 4
- total outcomes of 2 Heads = 6
- total outcomes of 3 Heads = 4
- total outcomes of 4 Heads = 1
This is very useful for tossing a large number of coins. You can save time from listing all possibilities.
Therefore, the probability of 2 coins land heads up:
[tex]\displaystyle P(A)=\frac{n(A)}{n(S)}[/tex]
[tex]\displaystyle =\frac{6}{16}[/tex]
[tex]\displaystyle=\bf\frac{3}{8}[/tex]
