Question

1) The following frequency distribution analyzes the scores on a math test. Find the probability that a score than $2 was achieved Interpret the folowngprobability statement using the frequentist interpretation of probability. The proformed in a month what can be concluded? this particular type of surgery will be successful. If 46 of these surgires are 3) In a competition, two people will be selected from four finalists to receive the first and second prizes. The winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows. G JH JM GJ GH GM Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The events A and B are defined as follows. A - event that Helen gets first prize B event that both prize winners are women List the outcomes that comprise the event (A & B)

Answer 1

${\color{Blue} \mathbf{7)}}$

$\mathbf{given:}\;n=11,p=0.5,q=1-p=0.5$

$\mathbf{formula:}\;P(X=r)=_{r}^{n}\textrm{C}*p^{r}*q^{n-r}\;\;where,\;\;_{r}^{n}\textrm{C}=\frac{n!}{r!(n-r)!}$

$P(X=6)=_{6}^{11}\textrm{C}*0.5^{6}*0.5^{11-6}$

$P(X=6)=\frac{11!}{6!(11-6)!}*0.5^{6}*0.5^{5}$

$P(X=6)=462*0.5^{6}*0.5^{5}$

$P(X=6)=\mathbf{{\color{Red} 0.2256}}$

--------------------------------------------------------------------------------------------

${\color{Blue} \mathbf{8)}}\;{\color{Red} \mathbf{What \;should \;i \;find?}}$