DISCRETE DISTRUBUTIONS. COMPLETE THE ENTIRE PARTS. I WILL LEAVE GOOD REVIEW

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P= probobility of prize coupons =0.15n= number of cups =10here the probability of winning is constant. at 0.15 and number of trials are finite & Independent. So use Binomial distributionBinomiol distribution\begin{array}{l}P(x=r)={ }_{c} c_{\gamma} q^{n-r} \quad n_{c_{\gamma}}=n ! \\\gamma !(n-\gamma) ! \\X \sim \operatorname{Bin}(n, \rho) \quad q=1-p \\n=10, p=0-15 \\=0.85 \\\end{array}a) x - number of prizes they win\begin{array}{l}P(x \geq 7)=P(x=7)+p(x=8)+p(x=9)+p(x=10) \\={ }^{10} c_{7}(0.15)^{7}(0.85)^{3}+10 c_{8}(0.15)^{8}(0.85)^{2}+10 c_{9}(0.15)^{9}(0.85) \\+{ }^{10} c_{10}(0.15)^{10}(0.85)^{\circ} \quad\left({ }^{10} c_{7}=\frac{10 !}{7 ! ! 3 !}=\frac{10 \times 9 \times 8 \times 7 !}{7 !+3 \times \times 1}\right. \\=120(0.15)^{7}(0.85)^{3}+45(0.15)^{8}(0.85)^{2} \\+10(0.15)^{9}(0.85)+1(0.15)^{10}(1) \\{ }_{8}^{10}=\frac{10 !}{8 ! 2 !}=\frac{\stackrel{=120}{=} \times 9 \times 8)}{8 !(2 \times 1)}=45 \\{ }^{10} c_{9}=\frac{10 !}{9 ! 1 !}=\frac{10 \times 9 !}{9 !}=10 \\=0.00013 \\{ }^{10} L_{10}=1 \\\text { CS } P(x \geqslant \text { pion } 0.0001 \\(\because n !=n(n-1) \cdots \\\end{array}b) Expected number of prizes\begin{aligned}E(x) & =n p \\n=10, \quad p & =0.15 \\E(x) & =10 \times 0-15 \\E(x) & =1.5\end{aligned}\mathrm{CS}Scanned withCamScanner ...